Hypergeometric Distribution Calculator

About this calculator

The hypergeometric distribution gives the probability of drawing exactly k successes in n draws taken without replacement from a finite population of size N that contains K successes overall. It differs from the more familiar binomial distribution precisely because each draw changes the population left behind — once you have pulled a winning ticket out of a jar, it is gone, and the odds for the next draw shift accordingly.

This makes it the right model for situations like drawing cards from a single deck without putting them back, quality-control auditors pulling a sample of items from a finished production batch to check for defects, lottery and raffle odds, and ecologists estimating a wild population's size using capture-recapture methods, where the same “sampling without replacement” logic applies to marked versus unmarked animals.

Enter your population size N, the number of successes K in that population, your sample size n and the target number of successes k, and this calculator returns the exact hypergeometric probability.